Independent Coverings and Orthogonal Colourings
Combinatorics
2022-01-11 v3
Abstract
In this paper, two open conjectures are disproved. One conjecture regards independent coverings of sparse partite graphs, whereas the other conjecture regards orthogonal colourings of tree graphs. A relation between independent coverings and orthogonal colourings is established. This relation is applied to find independent coverings of some sparse partite graphs. Additionally, a degree condition providing the existence of an independent covering in the case where the graph has a square number of vertices is found.
Cite
@article{arxiv.2008.07904,
title = {Independent Coverings and Orthogonal Colourings},
author = {Kyle MacKeigan},
journal= {arXiv preprint arXiv:2008.07904},
year = {2022}
}
Comments
10 pages, 6 figures